Introduction to graph theory and networks

Social connections are fundamental to society, including family ties, shared roles in communities, trading relationships, and many more. Social networks—from MySpace to Twitter to TikTok—have played a larger and larger role in marketing, job-hunting, and information sharing in the last decades. Software systems might even be built between engineers scattered across the globe collaborating on platforms such as GitHub or Slack to coordinate efforts from teams in Kenya, India, and Australia who have never met.

A branch of data science called network science studies these relationships between individuals, groups, and even societies within social networks using algorithms and statistical methods originating in a field of math called graph theory. Graph theory studies pairwise relationships between objects. Graph objects (including people, towns, ideas, points in time, and many more types of objects to study) are represented in...